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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_linear_regression.wasp
Title produced by softwareLinear Regression Graphical Model Validation
Date of computationMon, 15 Nov 2010 20:21:25 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/15/t12898524097qve8ggpie0yyh5.htm/, Retrieved Sat, 27 Apr 2024 18:07:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=95047, Retrieved Sat, 27 Apr 2024 18:07:50 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Paired and Unpaired Two Samples Tests about the Mean] [Dagelijkse omzet ...] [2010-10-25 11:22:12] [b98453cac15ba1066b407e146608df68]
-   PD  [Paired and Unpaired Two Samples Tests about the Mean] [question 5 T] [2010-10-29 12:27:53] [c1605865773cc027e55b238d879a644c]
-    D    [Paired and Unpaired Two Samples Tests about the Mean] [] [2010-11-01 09:41:08] [22937c5b58c14f6c22964f32d64ff823]
F           [Paired and Unpaired Two Samples Tests about the Mean] [Workshop 5 Questi...] [2010-11-01 15:47:21] [945bcebba5e7ac34a41d6888338a1ba9]
-             [Paired and Unpaired Two Samples Tests about the Mean] [] [2010-11-02 14:45:56] [5278e0a58c5de897b31ce79607e774d7]
- RMPD            [Linear Regression Graphical Model Validation] [Mini-Tutorial Hyp...] [2010-11-15 20:21:25] [67e3c2d70de1dbb070b545ca6c893d5e] [Current]
-    D              [Linear Regression Graphical Model Validation] [WS6 Minitutorial H1] [2010-11-15 20:32:21] [07a238a5afc23eb944f8545182f29d5a]
- R  D                [Linear Regression Graphical Model Validation] [ws 6 -minitutorial] [2010-11-16 17:45:24] [4eaa304e6a28c475ba490fccf4c01ad3]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
24
25
30
19
22
22
25
23
17
21
19
19
15
16
23
27
22
14
22
23
23
21
19
18
20
23
25
19
24
22
25
26
29
32
25
29
28
17
28
29
26
25
14
25
26
20
18
32
25
25
23
21
20
15
30
24
26
24
22
14
24
24
24
24
19
31
22
27
19
25
20
21
27
23
25
20
21
22
23
25
25
17
19
25
19
20
26
23
27
17
17
19
17
22
21
32
21
21
18
18
23
19
20
21
20
17
18
19
22
15
14
18
24
35
29
21
25
20
22
13
26
17
25
20
19
21
22
24
21
26
24
16
23
18
16
26
19
21
21
22
23
29
21
21
23
27
25
21
10
20
26
24
29
19
24
19
24
22
17
Dataseries Y:
Download CSV
Histogram 
23
15
25
18
21
19
15
22
19
20
26
26
21
18
19
19
18
19
24
28
20
29
27
18
19
24
21
22
25
19
15
34
23
19
26
15
15
17
30
19
28
23
23
21
18
19
24
15
20
24
9
20
20
10
44
20
20
20
11
21
21
19
21
17
16
14
19
21
16
19
19
16
24
29
21
20
19
23
18
19
23
19
21
26
13
23
16
17
30
19
22
14
14
21
21
33
23
30
19
21
25
18
29
25
21
16
17
23
26
18
19
28
20
29
19
18
25
15
24
12
11
19
25
12
15
25
14
19
23
19
24
20
16
13
20
30
18
22
21
25
18
25
44
12
28
17
26
18
21
24
20
24
28
20
33
19
19
25
35

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 6 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95047&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95047&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95047&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Simple Linear Regression
StatisticsEstimateS.D.T-STAT (H0: coeff=0)P-value (two-sided)
constant term14.80708379408072.290800198487716.463716828667851.22519838718915e-09
slope0.2833495247773860.1016321613835622.787990739545720.00595927027277354

\begin{tabular}{lllllllll}
\hline
Simple Linear Regression \tabularnewline
Statistics & Estimate & S.D. & T-STAT (H0: coeff=0) & P-value (two-sided) \tabularnewline
constant term & 14.8070837940807 & 2.29080019848771 & 6.46371682866785 & 1.22519838718915e-09 \tabularnewline
slope & 0.283349524777386 & 0.101632161383562 & 2.78799073954572 & 0.00595927027277354 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95047&T=1

[TABLE]
[ROW][C]Simple Linear Regression[/C][/ROW]
[ROW][C]Statistics[/C][C]Estimate[/C][C]S.D.[/C][C]T-STAT (H0: coeff=0)[/C][C]P-value (two-sided)[/C][/ROW]
[ROW][C]constant term[/C][C]14.8070837940807[/C][C]2.29080019848771[/C][C]6.46371682866785[/C][C]1.22519838718915e-09[/C][/ROW]
[ROW][C]slope[/C][C]0.283349524777386[/C][C]0.101632161383562[/C][C]2.78799073954572[/C][C]0.00595927027277354[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95047&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95047&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Simple Linear Regression
StatisticsEstimateS.D.T-STAT (H0: coeff=0)P-value (two-sided)
constant term14.80708379408072.290800198487716.463716828667851.22519838718915e-09
slope0.2833495247773860.1016321613835622.787990739545720.00595927027277354


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 5
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Figure 6
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Figure 7
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Figure 8
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Figure 9
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Input Parameters & R Code

Parameters (Session):
par1 = 0 ;
Parameters (R input):
par1 = 0 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
library(lattice)
z <- as.data.frame(cbind(x,y))
m <- lm(y~x)
summary(m)
bitmap(file='test1.png')
plot(z,main='Scatterplot, lowess, and regression line')
lines(lowess(z),col='red')
abline(m)
grid()
dev.off()
bitmap(file='test2.png')
m2 <- lm(m$fitted.values ~ x)
summary(m2)
z2 <- as.data.frame(cbind(x,m$fitted.values))
names(z2) <- list('x','Fitted')
plot(z2,main='Scatterplot, lowess, and regression line')
lines(lowess(z2),col='red')
abline(m2)
grid()
dev.off()
bitmap(file='test3.png')
m3 <- lm(m$residuals ~ x)
summary(m3)
z3 <- as.data.frame(cbind(x,m$residuals))
names(z3) <- list('x','Residuals')
plot(z3,main='Scatterplot, lowess, and regression line')
lines(lowess(z3),col='red')
abline(m3)
grid()
dev.off()
bitmap(file='test4.png')
m4 <- lm(m$fitted.values ~ m$residuals)
summary(m4)
z4 <- as.data.frame(cbind(m$residuals,m$fitted.values))
names(z4) <- list('Residuals','Fitted')
plot(z4,main='Scatterplot, lowess, and regression line')
lines(lowess(z4),col='red')
abline(m4)
grid()
dev.off()
bitmap(file='test5.png')
myr <- as.ts(m$residuals)
z5 <- as.data.frame(cbind(lag(myr,1),myr))
names(z5) <- list('Lagged Residuals','Residuals')
plot(z5,main='Lag plot')
m5 <- lm(z5)
summary(m5)
abline(m5)
grid()
dev.off()
bitmap(file='test6.png')
hist(m$residuals,main='Residual Histogram',xlab='Residuals')
dev.off()
bitmap(file='test7.png')
if (par1 > 0)
{
densityplot(~m$residuals,col='black',main=paste('Density Plot   bw = ',par1),bw=par1)
} else {
densityplot(~m$residuals,col='black',main='Density Plot')
}
dev.off()
bitmap(file='test8.png')
acf(m$residuals,main='Residual Autocorrelation Function')
dev.off()
bitmap(file='test9.png')
qqnorm(x)
qqline(x)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Simple Linear Regression',5,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistics',1,TRUE)
a<-table.element(a,'Estimate',1,TRUE)
a<-table.element(a,'S.D.',1,TRUE)
a<-table.element(a,'T-STAT (H0: coeff=0)',1,TRUE)
a<-table.element(a,'P-value (two-sided)',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'constant term',header=TRUE)
a<-table.element(a,m$coefficients[[1]])
sd <- sqrt(vcov(m)[1,1])
a<-table.element(a,sd)
tstat <- m$coefficients[[1]]/sd
a<-table.element(a,tstat)
pval <- 2*(1-pt(abs(tstat),length(x)-2))
a<-table.element(a,pval)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'slope',header=TRUE)
a<-table.element(a,m$coefficients[[2]])
sd <- sqrt(vcov(m)[2,2])
a<-table.element(a,sd)
tstat <- m$coefficients[[2]]/sd
a<-table.element(a,tstat)
pval <- 2*(1-pt(abs(tstat),length(x)-2))
a<-table.element(a,pval)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')